Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than π/6 and strictly smaller than π/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (aff...

Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 with coordinates in Fq. In this paper, we give a deterministic algorithm which computes the reduction of N(f) modulo pb in O(n(8m)(h+b)p) bit operations. This is singly exponential in each of the parameters {h, b, p}, ...

We developed an automatic blood pressure control system to maintain the blood pressure of patients at a substantially low level during a surgical operation. The developed system discharges two functions, continuous feedback control of the mean arterial pressure (MAP) by a state-predictive servo controller and risk control based on the inference by fuzzy-like logics and rules using measured data...

In this paper we answer two recent questions from Charlier et al. (2014) and Harju (2013) about self-shuffling words. An infinite word w is called self-shuffling, if w = ∏∞ i=0 UiVi = ∏∞ i=0 Ui = ∏∞ i=0 Vi for some finite words Ui, Vi. Harju recently asked whether square-free self-shuffling words exist. We answer this question affirmatively. Besides that, we build an infinite word such that no ...

Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably good and small summaries, they are inherently problem dependent — the practitioner has to commit to a fixed clustering objective before even exploring the data....

Several theories of grammar currently converge toward inserting subcategorization information within lexical entries. Such a tendency would benefit from a parsing algorithm able to work from "triggering positions" outward. In this paper a bidirectional extension of the chart algorithm is proposed and its most relevant formal properties are investigated using an Earley like formalism. The questi...

We prove that the Membership Problem is solvable affirmatively for every finitely generated quadratic module Q of R[X1]. For the case that the associated semialgebraic set S is bounded we show that a polynomial f is an element of Q if and only if f is nonnegative on S and fulfills certain order conditions in the boundary points of S. This leads us to the definition of generalized natural genera...

In this paper we consider the problem of finding upperbounds on the minimum norm of representatives in residue classes in quotient O/I, where I is an integral ideal in the maximal order O of a number field K. In particular, we answer affirmatively a question of Konyagin and Shparlinski, stating that an upperbound o(N(I)) holds for most ideals I, denoting N(I) the norm of I. More precise stateme...

We propose an algorithm that given as input a full word w of length n, and positive integers p and d, outputs, if any exists, a maximal pperiodic partial word contained in w with the property that no two holes are within distance d (so-called d-valid). Our algorithm runs in O(nd) time and is used for the study of repetition-freeness of partial words. Furthermore, we construct an infinite word o...

A recent extensive study has investigated how various exchange-correlation (XC) functionals treat hydrogen bonds in water hexamers and has shown traditional generalized gradient approximation and hybrid functionals used in density-functional (DF) theory to give the wrong dissociation-energy trend of low-lying isomers and van der Waals (vdW) dispersion forces to give key contributions to the dis...